# The area of four circles at the origin intersecting [duplicate]

I don't even know where to start. Do I need to find the width of the shaded areas, or something else completely?

UPDATE: Using the information given here, I was able to act as if the circles were inside of a square and use those methods.

Thank You

## marked as duplicate by user228113, RKD, GNUSupporter 8964民主女神 地下教會, Blue geometry StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Dec 10 '17 at 23:31

• By symmetry, integrate in polar coordinates from $0$ to $\pi/4$, then multiply by 8. The polar equation of the uppermost circle is $r=a\sin\theta$ for a circle of radius $a$. – Alexander Burstein Dec 10 '17 at 23:15